Math CentralQuandaries & Queries


Question from a student:

Suppose there are three firms with the same demand function. The function is Q=1000-40P. Each firm also a a cost function.
Firm 1: 4000+5Q
Firm 2: 3000+5Q
Firm 3: 3000+7Q

What price should each firm charge if it wants to maximize profits.

You know that the profit is maximized when the marginal cost (MC) is equal to the marginal revenue (MR) from your earlier question. If P is the price per unit, Q is the number of units sold then the revenue is Q x P. I assume that the cost function given is the total cost for producing Q items.  

Solve the demand function for P and then form the revenue function Q x P. For each firm find MC and MR, set them equal and solve for Q. Use the demand function to evaluate the price that each firm should charge.


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